A guitar string vibrates harmonically with a frequency of 512Hz (one octave abov

Question

A guitar string vibrates harmonically with a frequency of 512Hz (one octave above middle C on the musical scale). IF the amplitude of oscillation of the centerpoint of the string is .002. (2mm), what are the maximum speed and the maximum acceleration at that point? I understand how to get my max velocity(which I came up with 6.4339) But I have a difficult time understanding how to get the max acceleration at that point. A guitar string vibrates harmonically with a frequency of 512Hz (one octave above middle C on the musical scale). IF the amplitude of oscillation of the centerpoint of the string is .002. (2mm), what are the maximum speed and the maximum acceleration at that point? I understand how to get my max velocity(which I came up with 6.4339) But I have a difficult time understanding how to get the max acceleration at that point.

Explanation / Answer

A= 0.002m, f = 512 Hz At center point maximum velocity vmax = rw = A*2pf= 0.002* 2 *p *512= 6.4339 m/s Maximum acceleration is centripetal accleration = v2max /r = v2max /A

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